Maximise Your Money

"No," said Jennifer to her 14-year old son Kyle. "I do not feel inclined to increase your allowance by $10 per week. However, if you're willing to take a risk, I'll make you a sporting proposition."

"What is it this time, Mom?"

"I happen to have," Jennifer said, "ten crisp new one-dollar bills and ten crisp new ten-dollar bills. You may divide them any way you please into two sets. We'll put one set into hat A and the other set into hat B. Then I'll blindfold you. I'll mix the contents of each hat and place each one on the table. You pick either hat at random and then reach into the hat and withdraw one bill. If it's a ten you may keep it."

"And if it isn't?"

"You wash my van once a week for a month with no complaints."

Kyle agreed. How should he distribute the 20 bills into the two hats to maximize the probability of drawing a ten-dollar bill and what will that probability be?